What is the limit as t approaches 0 of (e^{-7t}-1)/t ?

The limit as t approaches 0 of (e^{-7t}-1)/t is -7

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limit as t approaches 0 of (e^{-7t}-1)/t

t \to 0 lim (\frac{e ^{- 7 t} - 1}{t})

- 7

Solution steps

t \to 0 lim (\frac{e ^{- 7 t} - 1}{t})

Apply L'Hopital's Rule

: t \to 0 lim (\frac{- 7 e ^{- 7 t}}{1})

= t \to 0 lim (\frac{- 7 e ^{- 7 t}}{1})

Plug in the value

t = 0

= \frac{- 7 e ^{- 7 \cdot 0}}{1}

Simplify

= - 7

x \to 0 lim (3 - 3 x + 6 x^{2})

x \to - 4 lim (\frac{2}{x ^{2} + 3 x - 4} - \frac{3}{x + 4})

x \to \infty lim ((\frac{1}{1 + \frac{5}{x}})^{x})

x \to 1 + lim (\frac{x}{x})

x \to 9 lim (\frac{lo g _{3} ( x ) ^{2} - 4}{lo g _{3} ( x ) - 2})

What is the limit as t approaches 0 of (e^{-7t}-1)/t ?
The limit as t approaches 0 of (e^{-7t}-1)/t is -7